This chapter introduces a unified stochastic modeling and simulation framework for blockchain-enabled robotic patient monitoring systems that integrate wearable sensors, edge analytics, robotic actuators, and Big Data pipelines. Layered mathematical models are developed to capture patient state evolution such as Markov chains and stochastic differential equations. It also records the noisy observation processes, robotic task scheduling (queueing models), network and blockchain confirmation delays, along with distributed processing latencies. Based on these models, a modular discrete-event simulation framework has been implemented to support reproducible experiments, and suitable statistical analysis. One representative case study with three sub-cases viz. (i) single-patient remote monitoring, (ii) multi-patient ward operations under permissioned consensus, and (iii) Big Data–driven anomaly detection, have been explored and evaluated. The attained results show that blockchain block time and the choice of consensus method strongly affect response delays. It also shows that the number of robots should match with the patient load to avoid long queues. The chapter ends with clear, practical guidelines on choosing consensus models, as well as splitting inference tasks, and building privacy-preserving data systems. Moreover, it has highlighted the key ethical and legal points to consider when using autonomous agents in healthcare systems.